In this paper we consider the problems of sensitivity analysis on fuzzy relation equations defined by x ∘ A = b where A is a state matrix and x, b are input and output vectors respectively with maxmin operator “∘”. When a state-matrix and an output-vector are given, the problems we concern are first how to determine the set of state-matrices which has the same solution set X(A, b) = {x | x ∘ A = b} with respect to a common output-vector? Second, when the solution set is empty how to determine the adjustable possibilities of the output-vector such that there exists at least one solution? By means of the defined quasi-characteristic matrix, the corresponding algorithms are proposed with numerical examples.